Extending potential flow modelling of flat-sheet geometries as applied in membrane-based systems
TL;DR: In this article, a flat-sheet geometries applied in membrane-based systems are used to calculate the residence time distribution of a chemical reaction, which depends mainly on the 2D velocity field, parallel to the membrane.
About: This article is published in Journal of Membrane Science.The article was published on 2008-12-01. It has received 19 citations till now. The article focuses on the topics: Residence time (fluid dynamics) & Residence time distribution.
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TL;DR: In this paper, the authors studied the power density and energy efficiency of a stack of 50 cells with a spacer thickness of 200 mu m and a cell resistance of 0.345 Omega.
354 citations
TL;DR: The fundamentals of the ED process are presented, highlighting limitations and potentialities in the water and energy industry and the most recent applications of ED-related processes are presented.
330 citations
TL;DR: This study shows the performance of a scaled-up RED stack, equipped with 50 cells, and shows that the use of segmented electrodes increase the power output by 11%.
Abstract: Electricity can be produced directly with reverse electrodialysis (RED) from the reversible mixing of two solutions of different salinity, for example, sea and river water. The literature published so far on RED was based on experiments with relatively small stacks with cell dimensions less than 10 × 10 cm(2). For the implementation of the RED technique, it is necessary to know the challenges associated with a larger system. In the present study we show the performance of a scaled-up RED stack, equipped with 50 cells, each measuring 25 × 75 cm(2). A single cell consists of an AEM (anion exchange membrane) and a CEM (cation exchange membrane) and therefore, the total active membrane area in the stack is 18.75 m(2). This is the largest dimension of a reverse electrodialysis stack published so far. By comparing the performance of this stack with a small stack (10 × 10 cm(2), 50 cells) it was found that the key performance parameter to maximal power density is the hydrodynamic design of the stack. The power densities of the different stacks depend on the residence time of the fluids in the stack. For the large stack this was negatively affected by the increased hydrodynamic losses due to the longer flow path. It was also found that the large stack generated more power when the sea and river water were flowing in co-current operation. Co-current flow has other advantages, the local pressure differences between sea and river water compartments are low, hence preventing leakage around the internal manifolds and through pinholes in the membranes. Low pressure differences also enable the use of very thin membranes (with low electrical resistance) as well as very open spacers (with low hydrodynamic losses) in the future. Moreover, we showed that the use of segmented electrodes increase the power output by 11%.
207 citations
TL;DR: The challenges still facing concerning the economic and technological feasibility and the developing path of reverse electrodialysis are discussed, with a focus on the development of low-cost membranes, pre-treatment in relation to stack design and operation, and the economics of reverseElectrolysis.
Abstract: Reverse electrodialysis is a conversion technique to obtain electricity from salinity gradients. Over the past few years, the performance of reverse electrodialysis on laboratory scale has improved considerably. In this paper, we discuss the challenges we are still facing concerning the economic and technological feasibility and the developing path of reverse electrodialysis. We focus on the following issues: (i) the development of low-cost membranes, (ii) pre-treatment in relation to stack design and operation, and (iii) the economics of reverse electrodialysis. For membranes, the challenge is to increase availability (>km2/year) at reduced cost (<2 €/m2). The membranes should be manufactured at high speed to meet this challenge. For pre-treatment, a capital-extensive microscreen filter with 50 μm pores was selected and tested. Such a straightforward pre-treatment is only suffi cient given the fact that the reverse electrodialysis stack was redesigned towards a more robust spacer-free system. For the eco...
156 citations
TL;DR: In this paper, the authors focused on the analysis of the overall performance of the SGP-RE process and the proper attention should be devoted to verify whether the spacer geometry optimi...
Abstract: Salinity Gradient Power by Reverse Electrodialysis (SGP-RE) technology allows the production of electricity from the different chemical potentials of two differently concentrated salty solutions flowing in alternate channels suitably separated by selective ion exchange membranes. In SGP-RE, as well as in conventional ElectroDialysis (ED) technology, the process performance dramatically depends on the stack geometry and the internal fluid dynamics conditions: optimizing the system geometry in order to guarantee lower pressure drops (ΔP) and uniform flow rates distribution within the channels is a topic of primary importance. Although literature studies on Computational Fluid Dynamics (CFD) analysis and optimization of spacer-filled channels have been recently increasing in number and range of applications, only a few efforts have been focused on the analysis of the overall performance of the process. In particular, the proper attention should be devoted to verify whether the spacer geometry optimi...
70 citations
References
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01 Jan 1980
TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.
Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.
21,858 citations
Book•
01 Jan 1967TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Abstract: Preface Conventions and notation 1. The physical properties of fluids 2. Kinematics of the flow field 3. Equations governing the motion of a fluid 4. Flow of a uniform incompressible viscous fluid 5. Flow at large Reynolds number: effects of viscosity 6. Irrotational flow theory and its applications 7. Flow of effectively inviscid liquid with vorticity Appendices.
11,187 citations
TL;DR: In this paper, the Navier-Stokes equation is derived for an inviscid fluid, and a finite difference method is proposed to solve the Euler's equations for a fluid flow in 3D space.
Abstract: This brief paper derives Euler’s equations for an inviscid fluid, summarizes the Cauchy momentum equation, derives the Navier-Stokes equation from that, and then talks about finite difference method approaches to solutions. Typical texts for this material are apparently Acheson, Elementary Fluid Dynamics and Landau and Lifschitz, Fluid Mechanics. 1. Basic Definitions We describe a fluid flow in three-dimensional space R as a vector field representing the velocity at all locations in the fluid. Concretely, then, a fluid flow is a function ~v : R× R → R that assigns to each point (t, ~x) in spacetime a velocity ~v(t, ~x) in space. In the special situation where ~v does not depend on t we say that the flow is steady. A trajectory or particle path is a curve ~x : R→ R such that for all t ∈ R, d dt ~x(t) = ~v(t, ~x(t)). Fix a t0 ∈ R; a streamline at time t0 is a curve ~x : R→ R such that for all t ∈ R, d dt ~x(t) = ~v(t0, ~x(t)). In the special case of steady flow the streamlines are constant across times t0 and any trajectory is a streamline. In non-steady flows, particle paths need not be streamlines. Consider the 2-dimensional example ~v = [− sin t cos t]>. At t0 = 0 the velocities all point up and the streamlines are vertical straight lines. At t0 = π/2 the velocities all point left and the streamlines are horizontal straight lines. Any trajectory is of the form ~x = [cos t + C1 sin t + C2] >; this traces out a radius-1 circle centered at [C1 C2] >. Indeed, all radius-1 circles in the plane arise as trajectories. These circles cross each other at many (in fact, all) points. If you find it counterintuitive that distinct trajectories can pass through a single point, remember that they do so at different times. 2. Acceleration Let f : R × R → R be some scalar field (such as temperature). Then ∂f/∂t is the rate of change of f at some fixed point in space. If we precompose f with a 1 Fluid Dynamics Math 211, Fall 2014, Carleton College trajectory ~x, then the chain rule gives us the rate of change of f with respect to time along that curve: D Dt f := d dt f(t, x(t), y(t), z(t)) = ∂f ∂t + ∂f ∂x dx dt + ∂f ∂y dy dt + ∂f ∂z dz dt = ( ∂ ∂t + dx dt ∂ ∂x + dy dt ∂ ∂y + dz dt ∂ ∂z ) f = ( ∂ ∂t + ~v · ∇ ) f. Intuitively, if ~x describes the trajectory of a small sensor for the quantity f (such as a thermometer), then Df/Dt gives the rate of change of the output of the sensor with respect to time. The ∂f/∂t term arises because f varies with time. The ~v ·∇f term arises because f is being measured at varying points in space. If we apply this idea to each component function of ~v, then we obtain an acceleration (or force per unit mass) vector field ~a(t, x) := D~v Dt = ∂~v ∂t + (~v · ∇)~v. That is, for any spacetime point (t, ~x), the vector ~a(t, ~x) is the acceleration of the particle whose trajectory happens to pass through ~x at time t. Let’s check that it agrees with our usual notion of acceleration. Suppose that a curve ~x describes the trajectory of a particle. The acceleration should be d dt d dt~x. By the definition of trajectory, d dt d dt ~x = d dt ~v(t, ~x(t)). The right-hand side is precisely D~v/Dt. Returning to our 2-dimensional example ~v = [− sin t cos t]>, we have ~a = [− cos t − sin t]>. Notice that ~v · ~a = 0. This is the well-known fact that in constant-speed circular motion the centripetal acceleration is perpendicular to the velocity. (In fact, the acceleration of any constant-speed trajectory is perpendicular to its velocity.) 3. Ideal Fluids An ideal fluid is one of constant density ρ, such that for any surface within the fluid the only stresses on the surface are normal. That is, there exists a scalar field p : R × R → R, called the pressure, such that for any surface element ∆S with outward-pointing unit normal vector ~n, the force exerted by the fluid inside ∆S on the fluid outside ∆S is p~n ∆S. The constant density condition implies that the fluid is incompressible, meaning ∇ · ~v = 0, as follows. For any region of space R, the rate of flow of mass out of the region is ∫∫ ∂R ρ~v · ~n dS = ∫∫∫
9,804 citations
Book•
30 Jun 1972TL;DR: An overview of Chemical Reaction Engineering is presented, followed by an introduction to Reactor Design, and a discussion of the Dispersion Model.
Abstract: Partial table of contents: Overview of Chemical Reaction Engineering. HOMOGENEOUS REACTIONS IN IDEAL REACTORS. Introduction to Reactor Design. Design for Single Reactions. Design for Parallel Reactions. Potpourri of Multiple Reactions. NON IDEAL FLOW. Compartment Models. The Dispersion Model. The Tank--in--Series Model. REACTIONS CATALYZED BY SOLIDS. Solid Catalyzed Reactions. The Packed Bed Catalytic Reactor. Deactivating Catalysts. HETEROGENEOUS REACTIONS. Fluid--Fluid Reactions: Kinetics. Fluid--Particle Reactions: Design. BIOCHEMICAL REACTIONS. Enzyme Fermentation. Substrate Limiting Microbial Fermentation. Product Limiting Microbial Fermentation. Appendix. Index.
8,257 citations
TL;DR: The thermal dispersion conductivity tensor for convection in a porous medium is derived based on the method of volume averaging of the velocity and temperature deviations in the pores.
619 citations